Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Flashcards Preview

Mei:CogSci Semester 2 > Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices > Flashcards

Flashcards in Statistics VI - PCA + Meta Exam Questions + Vectors/Matrices Deck (31):
1

What should the PCA be based on if all variables have the same units?

the covariance matrix

2

What should the PCA be based on if variables have different units?

the correlation matrix

3

In a PCA of a bivariate distributions: The coordination system is rotated so that ...

... the first axis - the first PC - has the largest possible variance.

4

How come we are allowed to rotate the coordination system in the PCA?

We are allowed to do that, because the total variance is invariant against rotation of data.

5

The sum of squared distances of a distribution = 3.224.
What is the sum of squared distances after rotating the data in the course of a PCA?

the same: 3.224

6

The second PC has the ___________ largest variance and is _________ to the first PC.

The second PC has the SECOND largest variance and is ORTHOGONAL to the first PC.

7

What's the total variance in the following (graphically akward) covariance matrix?
[0.950 0.647]
[0.647 0.820]

0.950 + 0.820 = 1.770

8

What multivariate tests should we know?

MANCOVA
MANOVA
Hotelling's T²

9

What univariate tests should we know?

student's t-test
ANOVA
ANCOVA

10

What is an eigenvector and an eigenvalue?

If A is a square matrix, v != 0 is an eigenvector of A, if
A * v = λ * v

The number λ is called the eigenvalue of A.

11

List at least 6 tests!

student's t-test
Hotelling's T²
ANOVA
ANCOVA
MANOVA
MANCOVA

12

What can the following tests be useful for:
t-test
ANOVA
ANCOVA

t-test: difference btw 2 groups and 1 variable
ANOVA: difference btw several groups, one dependent variable
ANCOVA: difference btw several groups, one dependent variable + controls

13

What can the following tests be useful for:
Hotelling's T²
MANOVA
MANCOVA

Hotelling's T²: difference btw 2 groups and several variables
MANOVA: several dependent variables, groups, interaction among variables
MANCOVA: several dependent variables, groups, interaction among variables + controls

14

How is the name of a vector usually written in statistics?

bold lowercase letter

15

How many columns does a vector have?

1

16

What's the difference between the vector v and the vector v'?

v is a column vector and
v' is the transposed version of vector v

17

In a matrix, what is represented through rows and columns?

rows: cases
columns: variables

18

How does M' look like if M =
(2 4 1)
(3 8 4)

(2 3)
(4 8)
(1 4)

19

What's the distinct property of a square matrix?

Same amount of rows and columns.

20

What's the distinct property of a symmetric matrix?

S = S'

21

What's the (main) diagonal of a matrix?

The "row" of numbers from top left to bottom right.

22

What is an identity matrix (aka. unit matrix)?

An identity matrix is a square matrix with ones on the main diagonal.

23

Cor(a,b) = 0.8
How large is the explained variance?

0.8² = 0.64 -> 64 %

24

Cor(a,b) = - 0.3
How large is the explained variance?

- 0.3² = 0.09 -> 9 %

25

What's the definition of discrete data?

Discrete Data can only take certain values.

26

What's the definition of continuous data?

Continuous Data is data that can take any value (within a range)

27

What kind of a scale is Kelvin?

ratio scale

28

What kind of a scale is Celsius?

interval scale

29

Define precision!

Degree to which repeated measurements show the same results

30

Define accuracy!

Closeness of measurements of a quantity to the quantity's actual (true) value.

31

Define bias!

Difference between the average of the measurements and the reference value.